CLASSIFICATION OF SOLUTIONS FOR A CLASS OF SINGULAR INTEGRAL SYSTEM  

作　　者：许建开 谭忠 

机构地区：[1]College of Sciences, Hunan Agriculture University [2]School of Mathematical Sciences, Xiamen University

出　　处：《Acta Mathematica Scientia》2011年第4期1449-1456,共8页数学物理学报（B辑英文版）

基　　金：Supported by National Natural Science Foundation of China-NSAF (10976026)

摘　　要：In this paper, we consider the following integral system： u（x） = R n v q （y） ｜ x y ｜ nα dy, v（x） = R n u p （y） ｜ x y ｜ nμ dy, （0.1） where 0 〈 α, μ 〈 n; p, q ≥ 1. Using the method of moving planes in an integral form which was recently introduced by Chen, Li, and Ou in [2, 4, 8], we show that all positive solutions of （0.1） are radially symmetric and decreasing with respect to some point under some general conditions of integrability. The results essentially improve and extend previously known results [4, 8].In this paper, we consider the following integral system： u（x） = R n v q （y） ｜ x y ｜ nα dy, v（x） = R n u p （y） ｜ x y ｜ nμ dy, （0.1） where 0 〈 α, μ 〈 n; p, q ≥ 1. Using the method of moving planes in an integral form which was recently introduced by Chen, Li, and Ou in [2, 4, 8], we show that all positive solutions of （0.1） are radially symmetric and decreasing with respect to some point under some general conditions of integrability. The results essentially improve and extend previously known results [4, 8].

关 键 词：Hardy-Littlewood-Sobolev inquality integral equation moving plane interpolation inequality radial symmetry 

分 类 号：O175.5[理学—数学]